# Algebra 2 / Trig Skills

Hi! I’m looking for some feedback on what skills I should use in my standards-based grading Algebra 2 with Trigonometry (A2T) course spring semester. I just threw together the following list as a rough draft, and do expect to edit it extensively over the coming week.

A note on organization: I’m planning to focus on algebra third quarter and analysis fourth quarter (did I miscategorize any skills?). Fourth quarter tends to be the shortest quarter, mainly due to our state standardized tests, so it has fewer skills. The first six skills each quarter are meant to be prerequisite skills from Algebra I, Geometry, or even middle-school math; I will hold students accountable for knowing and remembering these skills, but aside from a miniature review I do not intend to teach skills #1-6. I’ve italicized skills that seem weak or a little too easy, and may be combined with others or even eliminated. I’ve bolded skills that seem more advanced or non-essential and possibly not for every student. I’m toying with the idea of requiring students demonstrate mastery of certain numbers of core skills and advanced skills to earn different letter grades.

ALGEBRA (especially of the second degree)!

1. Graph a line given its equation
2. Determine the equation of a line from its graph
3. Solve a linear equation in any form
4. Solve a system of two linear equations
5. Manipulate algebraic expressions to simplify or expand
6. Substitute numbers for variables in an algebraic expression
7. Convert between scientific and standard notations of numbers
8. Apply the rules of exponents to simplify an expression
9. Find the degree and leading coefficient of a polynomial
10. Determine the end behavior of a function
11. Combine like terms to add or subtract polynomials
12. Use the distributive property to multiply polynomials
13. Use long division to divide polynomials
14. Factor a monic quadratic expression
16. Characterize the shape of a parabola given its equation
17. Graph a parabola given its equation
18. Determine the equation of a parabola given its graph
19. Solve quadratic equations in factored form using the zero product property
20. Solve quadratic equations in vertex form by isolating the variable
22. Solve quadratic equations in standard form by completing the square
23. Combine like terms to get an equation in standard form
24. Apply quadratic equations to physics or other real-world scenarios
25. Plot a complex number in the complex plane
26. Add and subtract complex numbers
27. Multiply complex numbers
28. Determine the magnitude of a complex number
29. Solve quadratic equations with complex roots
30. Add and subtract matrices, and multiply a matrix by a scalar
31. Multiply matrices
32. Find matrix determinants
33. Find the inverse of a matrix
34. Solve matrix equations
35. Solve systems of linear equations
36. Graph linear inequalities
37. Solve systems of linear inequalities by linear programming
38. Plot the graph of various conic sections based on its equation
39. Identify key characteristics of each conic section
40. Explain the relationship among the conic sections

ANALYSIS (including TRIGONOMETRY)!

1. Determine a function’s domain, range, maxima, and minima
2. Determine a function’s zeros and y-intercepts
3. Determine the end behavior of a function
4. Convert between tables of values, equations, and graphs of functions
5. Apply the Pythagorean Theorem to find unknown sides in right triangles
6. Use trigonometry to find unknown sides & angles in right triangles
7. Use laws of sines and cosines to find unknown sides & angles in any triangle
8. Solve entire triangles given three pieces of information
9. Apply triangular trigonometry to real-world scenarios
10. Draw and measure angles in standard position
11. Convert between degrees and radians
12. Find coordinates and slope where an angle meets the unit circle
13. Solve trigonometric equations (including multiple solutions)
14. Use common trigonometric identities
15. Sketch the graph of trigonometric functions
16. Find period and amplitude of periodic functions
17. Plot points using polar coordinates
18. Convert between polar and Cartesian coordinates
19. Plot various polar functions
20. Evaluate exponential expressions
21. Apply the rules of exponents to simplify an expression
22. Identify characteristics of exponential functions
23. Use exponential functions to model real-world scenarios
24. Convert between exponential and logarithmic equations
25. Evaluate logarithmic expressions
26. Apply the rules of logarithms to simplify an expression
27. Solve exponential and logarithmic equations
28. Use logistic growth to model real-world scenarios
29. Identify the effects of common function transformations
30. Graph functions and their inverses
31. Use inverse operations to solve equations
32. Compose functions
33. Discuss the effect of transforming, inverting, and composing functions on domain and range

I’m looking for feedback of any kind now, all the way from how to rephrase a skill better and more specifically, to what quintessential A2T skills are missing that I need to add right away. Also, are there some skills here that I can get rid of entirely? Even with the idea of prerequisite/core/advanced skills, 73 seems like way too many (I had only 32 skills this fall for geometry).

[PS I promise a post up soon reflecting back on what worked and what didn’t from semester 1’s courses, and looking ahead to my plans for the new semester’s courses, including how those plans reflect on SBG and PBL.]